Express this quotient in scientific notation: ${\frac{2.720\times 10^{-1}} {4.0\times 10^{-4}}}$
Start by collecting like terms together. $= {\frac{2.720} {4.0}} \times{\frac{10^{-1}} {10^{-4}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.68 \times 10^{-1\,-\,-4}$ $= 0.68 \times 10^{3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.68$ is the same as $6.80 \div 10$ , or $6.80 \times 10^{-1}$ $ = {6.80 \times 10^{-1}} \times 10^{3} $ $= 6.80\times 10^{2}$